Overview. This symposium on teacher effectiveness offers a comparative analysis of four studies that identified teaching practices that produce significant student learning in mathematics. In earlier work, the four studies took a range of approaches to studying effective mathematics teaching: two of the studies used assessment systems to identify high-quality instruction; one study examined how expert mathematics teachers contributed to the professional learning of novice mathematics teachers; and the fourth study analyzed the mathematics teaching of an expert teacher in an instructional intervention as part of a lab class open to observers.

This symposium builds on this earlier work. To date these four research projects have reported their individual findings regarding high-quality mathematics instruction. In this symposium, the four research projects endeavor to synthesize their findings across divergent data sources and methods, in order to identify with common language and definition categories of practices that characterize high-quality mathematics instruction. As a group, we present convergent findings as compelling evidence for a robust view of high-quality mathematics instruction, one that transcends context and method. For example, preliminary cross-project analysis indicates that in all four studies high-quality instruction is marked by teachers’ careful use of mathematical language. It is these kinds of convergent findings that will be presented in this symposium. We describe the principles that underlie high quality teaching, the knowledge that supports it, and the methods that comprise it. We argue that for the field to make significant contributions to the improvement of mathematics learning, a shared view of the features of high-quality mathematics instruction is imperative. We also describe where these research efforts yield divergent findings and what this means regarding efforts to improve instruction.

We note that although all four research projects study high-quality mathematics teachers, this is done in an effort to better understand and capture high-quality teaching. The intention is not to elevate individual persons or personalities, but to derive from the specifics of their individual and collective practices a generalized understanding of the qualities of effective mathematics instruction.

Theoretical Framework: The studies draw from different research traditions, although all share a sociocultural stance. All four studies have an empirical basis: they looked at the practice of teachers to identify the features of high-quality mathematics instruction.  And all the studies provide windows onto teaching practice but from different vantage points: two projects focused on classroom enactment/behaviors without particular access to our teacher's cognition; one included the additional and critical elements of teachers' reflections and conversations about their work; and one involved self-study, giving a fuller range of intention, enactment and reflection. We compare how the role of theory figures heavily into how teaching is specified and evaluated in each study. We trace how theory is used to construct our understandings of the teaching practices.

Data Sources: We compare differences in the initial criteria for identifying high-performing teachers and our respective sampling logic that helped us select the focal teachers to observe more closely. In two of the projects in this group, researchers used standardized test scores to identify high-quality teachers. In another study, the data are primarily the records of practice surrounding one expert teacher. In two of the studies, records of practice from a small set of high-quality teachers and the standardized test scores of their students comprise the data set. In one study, the research participants are a set of mentor teachers and the novice teachers with whom they work and the data are records of their teaching and interactions.

The symposium will allow participants to consider other possible indicators of high-quality instruction, for example carefully crafted and targeted assessments, open-ended tasks with a well-designed rubric, or analysis of students' mathematical talk in class.

Methods: All the studies analyze records of enacted classroom teaching as a way to identify high-quality mathematics teaching practices. The symposium highlights similarities and differences in observational methods of coding classroom interactions and the chains of reasoning that led researchers to infer that particular teaching practices could plausibly account for increased student learning.

Results. The analysis in the symposium includes identifying areas of convergence and divergence across the studies and how these both conform to and diverge from popular images of reform-oriented classrooms. We discuss choices in the grain-size of the teaching practices that were investigated.

Educational Importance of the Research: In a field where there is little agreement on what constitutes high-quality teaching, there is broad and overwhelming consensus that mathematics learning and achievement in this country is inadequate. This symposium contributes to the improvement of mathematics instruction by identifying, across a set of divergent studies, the features of high-quality mathematics instruction through a systematic analysis of classroom practice.

Organization of the Session

The session will be organized in a way that emphasizes synthesis across the four different research projects. The presenters from the four different research projects will not speak about their respective projects; instead, each presenter will speak about one aspect that runs across the four projects and will speak comparatively and synthetically across that topic.  For example, one presenter will talk about the methods used in all four projects, another will speak about the data sources used in all four projects, and so on.

Session overview: 5 minutes

Comparison across four studies on four topics: 60 minutes total

Methods: 15 minutes

Data sources: 15 minutes

Categories of high-quality teaching practice: convergence of findings; 15                                   minutes

Use in our own practices: 15 minutes

Comments from the discussant: 10 minutes

Discussion with audience: 30 minutes

This discussion will be framed by the following four discussion questions:

What is missing from the composite analysis of high-quality teaching presented here?

What methodological issues need to be addressed in the different projects presented?

How might these categories of high-quality teaching be used in teacher education?

What are the possibilities and limitations of cross-project efforts such as this one?

The discussant, a mathematician and mathematics educator, will provide critical review of the work with particular attention to the mathematical quality of instruction described in each study and across studies.